Range of the first three eigenvalues of the planar Dirichlet Laplacian

Michael Levitin; Rustem Yagudin

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Range of the first three eigenvalues of the planar Dirichlet Laplacian

Michael Levitin·Rustem Yagudin

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Abstract

We conduct extensive numerical experiments aimed at finding the admissible range of the ratios of the first three eigenvalues of a planar Dirichlet Laplacian. The results improve the previously known theoretical estimates of M Ashbaugh and R Benguria. We also prove some properties of a maximizer of the ratio $\lambda_3/\lambda_1$.

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Michael Levitin, Rustem Yagudin. 2002-03-22. Range of the first three eigenvalues of the planar Dirichlet Laplacian. https://arxiv.org/abs/math/0203231

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